Introduction to Physics for Mathematicians
by Igor Dolgachev
Number of pages: 285
A set of class notes in Introduction to Physics taken by math graduate students. The goal of this course was to introduce some basic concepts from theoretical physics which play so fundamental role in a recent intermarriage between physics and pure mathematics. No physical background was assumed.
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by Pavel Bleher, Alexander Its - Cambridge University Press
The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.
by Peter B. Gilkey - Publish or Perish Inc.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas and the Gauss-Bonnet theorem.
by J.F. Carinena, J. de Lucas - arXiv
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping.
by Young Suh Kim (ed.) - MDPI AG
With a degree of exaggeration, modern physics is the physics of harmonic oscillators and two-by-two matrices. Indeed, they constitute the basic language for the symmetry problems in physics, and thus the main theme of this journal.